Mean field equations, hyperelliptic curves and modular forms: I

Ching-Li Chai, Chang-Shou Lin, Chin-Lung Wang

We develop a theory connecting the following three areas: (a) the mean field equation (MFE) $△u+e^u=\rho {\delta }_0$, $\rho \in {\mathbb{R}}_{>0}$ on flat tori $E_τ= \mathbb C/(\math…